{"ID":23021120,"CreatedAt":"2026-09-17T04:55:43.771560302Z","UpdatedAt":"2026-09-17T04:55:43.771560302Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18806","arxiv_id":"2609.18806","title":"Fast Evaluation of the Sixth-Order Time-Convolutionless Master-Equation Generator and Beyond","abstract":"Direct quadrature of the Hadamard-reduced sixth-order time-convolutionless (TCL6) generator at all $N_t$ sampled times requires $O(N_t^3)$ operations at fixed system dimension. We derive an exact reduction for a finite-dimensional system coupled through one Hermitian operator to a stationary centered Gaussian bath. By separating fixed operator coefficients from scalar bath kernels, the complete TCL6 time series is reduced to cumulative sums and first-order recurrences, one-dimensional causal convolutions, and an exact dyadic recursion for interlocked histories. With the algorithm, evaluating the complete TCL6 time series requires $O(N_t\\log^2 N_t)$ operations at fixed system dimension. In addition, we show that TCL$2n$ can be evaluated with $O(N_t\\log^{n-1} N_t)$ complexity. A fixed finite Matsubara expansion of the bath correlation function permits $O(N_t\\log N_t)$ evaluation at any fixed TCL order. These reductions enable fast long-time simulations of non-Markovian open quantum systems within the regime of validity of the TCL expansion.","short_abstract":"Direct quadrature of the Hadamard-reduced sixth-order time-convolutionless (TCL6) generator at all $N_t$ sampled times requires $O(N_t^3)$ operations at fixed system dimension. We derive an exact reduction for a finite-dimensional system coupled through one Hermitian operator to a stationary centered Gaussian bath. By...","url_abs":"https://arxiv.org/abs/2609.18806","url_pdf":"https://arxiv.org/pdf/2609.18806v1","authors":"[\"Jiahao Chen\",\"Sirui Chen\",\"Dragomir Davidovic\"]","published":"2026-09-16T15:19:20Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"physics.comp-ph\"]","methods":"[]","has_code":false}